Further studies on wave propagation in overhead lines with earth return: impedance of stratified earth

A more rigorous and general solution for the earth-return impedance of overhead transmission lines than those given by Carson, Wise et al. is developed in the paper. In particular, the solution derived permits the earth-return path to be considered as three layers of differing resistivities, permittivities and permeabilities. The solution agrees with those previously derived under the same given conditions. Calculated results are presented to show the effects of the various parameters of the formulation developed. A stratified earth causes marked differences in the earth impedances and the resultant wave deformations from the homogeneous case. The depth of a layer is a significant factor to the value of the stratified-earth impedance. In comparison with the findings of earlier work, studies based on the formulation of the present paper indicate that, although displacement currents can influence earth-return impedances, this is only likely at frequencies in excess of 1 MHz and under the conditions of high earth resistivity and low conductor height. The effect of a ferromagnetic earth layer is shown to be significant at low frequencies. The attentuation of travelling waves is much less than that for the ordinary earth.